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LREtools

  

constcoeffsol

  

find all solutions of linear recurrence equations with constant coefficients

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

constcoeffsol(problem)

Parameters

problem

-

problem statement or RESol for a single equation in a single recurrence variable

Description

• 

Finds all solutions of the linear recurrence equation with constant coefficients.

• 

Optionally, one can specify output=basis  or output=gensol, which specifies respectively that one wants a basis of the solutions or a generic solution.  The initial conditions that may be associated to the problem are only used in the generic solution case.  Arbitrary constants for the basis case are represented as _C[1], _C[2], ..., _C[n], where the _C is an escaped local variable.

• 

See the help page for LREtools[REcreate] for the definition of the format of a problem.

Examples

withLREtools:

recan9an+1+26an+234an+3+21an+45an+5=0:

constcoeffsolrec,an,

153125256a43125256a0+312564a19375128a2+312564a315n+1654a4+14a02a1+92a24a3n+1n+2n+3128516a4+2116a0414a1+1758a2734a3n+1n+2+56564a4+18164a034116a1+134332a251716a3n+11845256a4821256a0+146164a15023128a2+178164a3

(1)

recan+4=an+3+3an+2+5an+1+2an:

constcoeffsolrec,an,

2154a3118a2118a1154a02n+1327a349a2+149a1+6827a01n+1213a3+a1+23a01nn+1n+2+79a3+13a283a1209a01nn+1

(2)

recan+22an+1an=0:

constcoeffsolrec,an,

14_α=RootOf_Z2+2_Z13a0+a1_α+a0a1_αn_α

(3)

See Also

LREtools

LREtools[REcreate]

RESol

rsolve

 


Download Help Document

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